There is nothing illogical about an infinite future, but since an infinite can never be reached, you can never say that it will have no definite end. You can only logically say that it could potentially have no end.

Short answer - no, everything that has a beginning does not have to have an end.

"Every kid starts out as a natural-born scientist, and then we beat it out of them. A few trickle through the system with their wonder and enthusiasm for science intact." - Carl Sagan

This is the response of the defenders of Sparta to the Commander of the Roman Army: "If you are a god, you will not hurt those who have never injured you. If you are a man, advance - you will find men equal to yourself. And women.

Pi is numerically endless. It has a well defined size, however. (~3.14...it's never going to be more than 3.15, so it is not endless, other than how it is represented numerically)

Pi has no end. Albeit that it does not get larger as you calculate further, it will always remain between 3.14 and 3.15. As you calculate it further, it just becomes more precise. But there is no end to its possible precision. It has no end, but it has a beginning, so it fits the question.

And I was not aware that there was a dichotomy between something being theoretical and numerical.

"Every kid starts out as a natural-born scientist, and then we beat it out of them. A few trickle through the system with their wonder and enthusiasm for science intact." - Carl Sagan

This is the response of the defenders of Sparta to the Commander of the Roman Army: "If you are a god, you will not hurt those who have never injured you. If you are a man, advance - you will find men equal to yourself. And women.

Pi is numerically endless. It has a well defined size, however. (~3.14...it's never going to be more than 3.15, so it is not endless, other than how it is represented numerically)

Pi has no end. Albeit that it does not get larger as you calculate further, it will always remain between 3.14 and 3.15. As you calculate it further, it just becomes more precise. But there is no end to its possible precision. It has no end, but it has a beginning, so it fits the question.

And I was not aware that there was a dichotomy between something being theoretical and numerical.

Pi is numerically endless. It has a well defined size, however. (~3.14...it's never going to be more than 3.15, so it is not endless, other than how it is represented numerically)

Pi has no end. Albeit that it does not get larger as you calculate further, it will always remain between 3.14 and 3.15. As you calculate it further, it just becomes more precise. But there is no end to its possible precision. It has no end, but it has a beginning, so it fits the question.

And I was not aware that there was a dichotomy between something being theoretical and numerical.

Pi is numerically endless. It has a well defined size, however. (~3.14...it's never going to be more than 3.15, so it is not endless, other than how it is represented numerically)

Pi has no end. Albeit that it does not get larger as you calculate further, it will always remain between 3.14 and 3.15. As you calculate it further, it just becomes more precise. But there is no end to its possible precision. It has no end, but it has a beginning, so it fits the question.

And I was not aware that there was a dichotomy between something being theoretical and numerical.

Pi very much has an end. Know how I know?

pi - pi = 0

infinity - infinity also = 0

Heh. Funny seeing that after our debate :P

"Music is a zen-like ecstatic state where you become the new man of the future, the Nietzschean merger of Apollo and Dionysus." Ray Manzarek (The Doors)